This invention relates to the field of seismic data processing and in particular to a method for moveout-correcting seismic data having non-hyperbolic moveout at longer offsets. Uses of the invention include, without limitation, pre-stack data analysis for AVO applications.
AVO is an abbreviation for Amplitude versus Offset, or, as it is sometimes written, amplitude variation with offset. AVO is a seismic data analysis method based on studying the variation in the amplitude of reflected waves with changes in the distance (offset) between the seismic source and receiver. The AVO response of the reflection events associated with the boundaries between the reservoir rock and the surrounding sealing materials often depends on the properties of the fluid stored in the reservoir pore space. Because of this property, AVO analysis is often used as a tool for reservoir fluid prediction.
AVO analysis is performed on Common-Depth-Point (CDP) gathers. Seismic events observed in CDP gathers exhibit a curvilinear shape (moveout). In order for the AVO method to be practically applicable to large data volumes, the gather has to be transformed (moved-out), so that the reflection events become horizontal (flat). In standard practice, this is performed using the Normal Moveout (NMO) method, which assumes that the original moveout of the reflection events is hyperbolic. This assumption works well for a small range of recorded offsets (usually up to about 3km). But for longer-offset gathers that are now commercially feasible to acquire and necessary for effective AVO analysis and reservoir properties prediction, the assumption is not adequate; events exhibit non-hyperbolic moveout over the longer offset ranges. An example is provided in FIGS. 1A and 1B. The picked reflection event 10 in FIG. 1A is flattened only over a limited range of offsets after NMO in FIG. 1B. In analyzing the AVO behavior of such data, the valuable far offsets have to be discarded; if they are included without proper flattening, there is a risk of wrong fluid type prediction. There is, therefore, a need for an efficient method that takes into account the non-hyperbolic moveout of the reflection events and flattens them over the complete range of offsets.
Non-hyperbolic reflection moveout has been recognized as a significant problem for a long time, and a large body of geophysical literature has been devoted to it. Current solutions fall into the following categories.
Different Approximations Used for the Moveout of Reflection Events
Normal-moveout is based on the hyperbolic approximation       t    2    =            t      0      2        +                  (                  X          V                )            2      
where t is the reflection time at an offset X, t0 the zero-offset time for the same reflection and V the Normal-Moveout (NMO) velocity. (Notwithstanding the preceding common terminology, it should be understood that V and t0 are not necessarily physically meaningful, but rather merely parameters that characterize the observations.) This approach is implemented in standard velocity-analysis packages where measures of reflection signal coherency (semblance) are calculated along hyperbolic trajectories through the seismic data. Trajectories corresponding to maximum coherency (semblance peaks) correspond to seismic events. Identifying the semblance peaks on 2-dimensional velocity analysis displays allows determination of the Normal-Moveout velocity V. If the parameter t0 is changed, then a different value of V will correspond to the semblance peaks. Thus V can be considered to be a function of t0, or V(t0).
A commonly adopted method for extending the validity of this equation to longer offsets is the use of the truncated 4-th order Taylor series expansion. (See, for example, Gidlow, P. M., and Fatti, J. L., 1990, xe2x80x9cPreserving far offset seismic data using non-hyperbolic moveout correctionxe2x80x9d, Expanded Abstracts of 60th Ann. Int. SEG Mtg., 1726-1729.) This approach is commercially available in the data processing systems of most seismic contractors. The equation used is:       t    2    =            t      0      2        +                  (                  X          V                )            2        -                  (                  X          W                )            4      
For each zero-offset time to, two parameters, V and W, need to be defined. Extending the standard semblance-based velocity analysis method to this case would imply picking peaks in 3-dimensional semblance panels (one for each CDP location, the three axes being time, V and W). This would be cumbersome and require special graphics. For this reason the most common approach is to first get an estimate of V, using the near offset data, then fix V and estimate W and then repeat the process until satisfactory alignment of the events has been achieved. The disadvantage of such an approach is that its application is time-consuming, because several iteration steps may be required for converging to a good set of coefficients for 2-nd and 4-th order terms.
Tsvankin and Thomsen derived an expression which they claimed to be an improvement upon the Taylor expansion formula in the presence of velocity anisotropy (wave velocity different for different propagation directions). (Tsvankin, I., and Thomsen, L., 1994, xe2x80x9cNonhyperbolic reflection moveout in anisotropic mediaxe2x80x9d, Geophysics, 59, 1290-1304.) This expression was re-written by Alkhalifah. (Alkhalifah, T., 1997, xe2x80x9cVelocity analysis using nonhyperbolic moveout in transversely isotropic mediaxe2x80x9d, Geophysics, 62, 1839-1854.) Their expression is:       t    2    =            t      0      2        +                  X        2                    V        2              -                  2        ⁢        η        ⁢                  xe2x80x83                ⁢                  X          4                                      V          2                ⁡                  [                                                    t                0                2                            ⁢                              V                2                                      +                                          (                                  1                  +                                      2                    ⁢                    η                                                  )                            ⁢                              X                2                                              ]                    
where xcex7 is an effective anisotropy parameter and V is the NMO velocity.
In addition to the above formulas, other types of equations have been proposed. Byun et al. introduced a xe2x80x9cskewedxe2x80x9d hyperbolic moveout formula. (Byun, B. S., Corrigan, D., and Gaiser, J. E., 1989, xe2x80x9cAnisotropic velocity analysis for lithology discriminationxe2x80x9d, Geophysics, 54, 1564-1574.) Castle and de Bazelaire proposed the use of a shifted-hyperbola equation. (Castle, R. J., 1994, xe2x80x9cA theory of normal moveoutxe2x80x9d, Geophysics, 59, 983-999; de Bazelaire, E., 1988, xe2x80x9cNormal moveout revisited: Inhomogeneous media and curved interfacesxe2x80x9d, Geophysics, 53, 143-157.) Yilmaz proposes the use of parabolas to describe the residual moveout of reflections after NMO has been applied. (Yilmaz, O., 1989, xe2x80x9cVelocity-stack processingxe2x80x9d, Geophysical Prospecting, 37, 351-382.)
All of the above methods suffer from the following shortcomings:
Non-hyperbolic moveout can be caused by vertical velocity heterogeneity, curvature of the reflecting horizon, lateral velocity variation and velocity anisotropy. Given this number of factors and the geologic complexity of the subsurface, it is unlikely that a single mathematical expression can provide a universal description applicable to all situations. Locations where reflection events exhibit anomalous moveout are often the places where hydrocarbon traps exist (vicinity of faults, salt domes). Failure of moveout algorithms to work adequately under such situations is a significant defect.
Even in cases when such algorithms can work, their application can be cumbersome and time-consuming, because several iteration steps may be required for determining the parameters included in the expressions (see the comments on the truncated Taylor series approach above).
Depth Migration with Detailed Subsurface Velocity Models
Since non-hyperbolic moveout is caused by geologic complexity and heterogeneity, an imaging method that can handle those complications accurately should be able to produce CDP gathers with flattened reflection events. Depth migration is the most accurate imaging method available today, and algorithms are available that can deal with velocity anisotropy and heterogeneity. Yet, depth migration is extremely sensitive to the accuracy of the velocity model used for imaging and very expensive to do in a manner that preserves AVO information. Numerous publications exist on methods for determining velocity models for depth migration. The basic scheme in such methods is to depth migrate with an initial velocity model, inspect the results, modify the velocity model and migrate again, performing a number of iterations until reflection events in CDP gathers are flat. This process is extremely time consuming and usually requires geologic input for constructing adequate velocity models.
Near-surface Correction Models
In situations where non-hyperbolic moveout is caused by topographic relief or near-surface heterogeneity (for example presence of shallow gas, permafrost), methods are available to address the problem. Of course, such methods will be effective only if near-surface heterogeneity is the only cause of non-hyperbolic moveout and if the near-surface properties are known with a high degree of accuracy.
Automatic Event Detection Methods
Such methods do not assume any model for the moveout of reflection events. Rather, they use pattern recognition techniques to track the events in the data. Once the events are tracked, they can be flattened using time shifting. An example of such a method is the one proposed by Boyd et al. (See U.S. Pat. No. 5,128,899.) The problem with such methods is that they fail to work adequately under the presence of noise, since noise can easily cause erroneous event tracking.
In view of the preceding description of current technology, a need exists for a method that:
Is generally applicable for addressing non-hyperbolic moveout problems, independent of the geologic factor causing non-hyperbolic moveout. The method should work adequately even for areas of large geologic complexity, large source-to-receiver offsets and large amounts of velocity anisotropy.
Is efficient to apply, because it is not based on an iterative procedure.
Is based on familiar velocity analysis tools and displays, readily available in most commercial processing packages.
The present invention satisfies these needs.
In one embodiment, the invention is a method for moveout-correcting a common-depth-point (CDP) gather of seismic data where the range of offsets is large enough that the moveout is nonhyperbolic for the longer offsets, which method comprises the steps of (a) dividing the offsets into discrete ranges, (b) fitting an analytical function for reflection time as a function of offset within each offset range, (c) combining these functions, enforcing continuity at range boundaries, into a single, piecewise-continuous function, and (d) moveout-correcting the seismic data using the piecewise-continuous function.
Hyperbolic functions are used in some embodiments of the invention; others use quartic polynomials or a combination of hyperbolic and quartic. Higher-degree polynomials or other functions may be used. Preferred embodiments of the invention use hyperbolic or quartic velocity analysis in forms currently available in standard seismic processing packages. The invention includes methods for flattening the reflection events over all offsets with a minimum number of offset ranges, thereby speeding up the process further.
The invention also includes methods for efficiently moving out the seismic data to offset the increase in computation time due to using more than one velocity function for moveout. Curves called pseudo-horizons are generated from the piecewise-continuous velocity function, and moveout is accomplished in some embodiments by interpolating between the pseudo-horizons.
In another embodiment, before horizon-based moveout, the input trace is interpolated to a finer sampling interval using high precision interpolation such as frequency-domain, sinc-function interpolation.
Potential uses of the present invention include AVO (Amplitude vs. Offset) applications.